I have a question. It's not clear to tell that what you are asking for. Are you asking for this:
[tex]\lim_{n \rightarrow \infty} \sqrt{n - \sqrt{n}} - \sqrt{n}[/tex]
or this:
[tex]\lim_{n \rightarrow \infty} \frac{\sqrt{n - \sqrt{n}} - \sqrt{n}}{\sqrt{n}}[/tex]?
If it's the latter, then you are correct!